Imaging system, method, and applications

ABSTRACT

A multicamera panoramic imaging system having no parallax. In an example, the multicamera panoramic imaging system includes multiple discrete, imaging systems disposed in a side-by-side array, wherein a field of view of each discrete, imaging systems is conjoined with a field of view of each adjacent discrete imaging system, further wherein a stencil of chief rays at the edge of the field of view of any one of the discrete imaging systems will be substantially parallel to a stencil of chief rays at the edge of the field of view of any adjacent ones of the discrete imaging systems such that all of the substantially parallel stencils of chief rays appear to converge to a common point when viewed from object space. A method for forming an image of an object having no parallax.

RELATED APPLICATION DATA

The instant application is a continuation application of U.S.application Ser. No. 17/742,964, which is a continuation application ofU.S. application Ser. No. 16/845,721, now U.S. Pat. No. 11,363,194,which is a continuation application of U.S. application Ser. No.16/420,752, now U.S. Pat. No. 10,659,688, which is a continuationapplication of U.S. application Ser. No. 15/309,180, now U.S. Pat. No.10,341,559 B2, which is a 371 of international application No.PCT/US2015/029146, which claims the benefit of U.S. provisionalapplication No. 61/989,136 filed May 6, 2014, the subject matter ofwhich is incorporated herein by reference in its entirety.

BACKGROUND Field of the Invention

Aspects and embodiments of the invention are most generally directed toan optical imaging system, methods pertaining thereto, and applicationsthereof; more particularly to a panoramic optical imaging system,methods pertaining thereto, and applications thereof; and, mostparticularly to a panoramic optical imaging system that has zero orsubstantially no parallax, methods pertaining thereto, and applicationsthereof.

Description of Related Art

Current 360 degree systems without parallax employ an arrangement ofmirrors to scan the image and are limited by an imaging speed of 10frames per second (fps). Google uses a 360 degree camera with refractivelenses developed by Immersive Media to capture photos for its Streetviewsoftware. The photos must be post-processed and corrected for parallax,costing time, which reduces Google's ability to scale its Streetviewinitiatives. Fisheye lenses provide wide angle imaging but at the costof high distortion. Distortion is the physical result of mapping a largespherical object onto a small flat image plane.

Some companies have developed optical systems to simplify the process oftaking a panoramic image. Rather than rotating the camera to getmultiple shots, all of the photos are captured simultaneously with manycameras imaging different parts of the scene. Immersive Media andGreypoint Imaging have developed single shot 360 degree cameras that areavailable for varying price tags between $10,000 and $100,000. Bothcompanies develop software to automatically correct for the artifacts(parallax) created in the image and offer a better solution thanpanoramas captured by one camera, e.g., the iPhone camera. The software,however, is not perfect and many artifacts still exist in the images.Anecdotally, Google, had one person carry a Dodeca 360 camera (offeredby Immersive Media) around the Grand Canyon, and had to employprogrammers to correct the images frame by frame for the artifactsinduced by parallax.

Parallax and the Chief Rays of an Optical System

Parallax is defined as “the effect whereby the position or direction ofan object appears to differ when viewed from different positions, e.g.,through the viewfinder and the lens of a camera.” Parallax is created asa result of stitching together images from multiple cameras, each withits own unique perspective of the world.

Referring to FIG. 1 , the chief ray 20 of an optical system 10 is themeridional ray that starts at the edge of an object 12, crosses thecenter of the optical axis 16 at the aperture stop 18, and ends at theedge of the image 14 at the detector. Thus, the chief ray defines thesize of an image.

The chief ray plays a critical role in the parallax created by stitchingtogether multiple images. FIG. 2 illustrates two optical systems(cameras) 25 side by side. For the lens unit on top, the square,triangle, and rectangle are mapped to the same point in the image,whereas for the lens unit on bottom they are mapped to three distinctpoints as shown. In the top imaging system they are imaged by the samechief ray 20, whereas for the bottom imaging system, they are imaged bythree distinct chief rays. When combining the two images 14 in FIG. 3 ,parallax would occur and an image 14 as shown in FIG. 4 would result.

The search for an algorithm that can correct for parallax has been goingon for many years. Many solutions have been developed but even with themost sophisticated algorithms to date, artifacts are still left inpanoramic images. For some, this may not be a problem as softwareengineers can be hired to fix the images frame by frame; however, forthe general consumer this option of correcting each image is notfeasible. A better solution is needed that effectively corrects forparallax before such a system can be made available to the consumermarket. It is preferable to solve the problem of reducing parallax in animage optically, rather than computationally.

Current designs created for single shot panoramic imaging suffer fromparallax because they are created from imaging systems with overlappingfields of view. FIG. 5 is taken from U.S. Pat. No. 2,696,758. Thisfigure illustrates how parallax is created in the 360 degree imagingsystems 50 available today. The field of views 28 overlap and a trianglethat appears at the edge of the FOV 28 for the bottom lens system willappear at around 0.707 times the FOV 28 in the imaging system on top.Thus, the triangle is mapped to different image points for each camera25. On the bottom it is mapped to the full FOV 28 (the edge of theimage).

The inventor has thus recognized the advantages and benefits of apanoramic imaging system and associated methods in which there is noparallax, and where the parallax is eliminated optically rather than bypost-processing software. Such a system would have applicationsincluding providing a scalable way to map the streets of the planet;allowing for the creation of virtual tours, both of cities and ofprivate institutions; high frame-rate video surveillance; militaryapplications including drone and tank technology; an alternative forfisheye lenses which provide wide angle imaging at the cost of highdistortion.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates the chief ray of an optical system. The chief raydefines the height of the object as well as the height of the image.

FIG. 2 illustrates why parallax occurs when multiple refractive imagingsystems are used to capture an image of a scene. In the lens unit ontop, the three objects are mapped to the same image point; in the bottomlens unit they are mapped to three separate image points.

FIG. 3 (left) illustrates the image formed by the top lens unit in FIG.2 , whereas the image on the right is that formed by the bottom lensunit.

FIG. 4 shows the image that would result from combining the two imagesin FIG. 3 .

FIG. 5 illustrates how parallax occurs in the cameras created today. Thefield of views overlaps and a triangle that appears at the edge of theFOV for the bottom lens system will appear at around 0.707 times the FOVin the imaging system on top. Thus, the triangle is mapped to differentimage points for each camera. On bottom it is mapped to the full FOV(the edge of the image).

FIG. 6 illustrates two imaging systems side by side which do not haveparallax. The chief rays at the edge of each system are constrained tolie parallel one another. Thus, objects lying along this line are imagedto the same point in the image plane.

FIG. 7 illustrates the location of the non-parallax (NP) Point (asdefined below) for both imaging systems shown.

FIG. 8 shows that the chief rays 20 at the edge of the FOV 28 are notparallel, thus the NP Points 60 lie in different locations.

FIG. 9 illustrates an imaging system with NP Point lying before imagesensor.

FIG. 10 illustrates two imaging systems aligned such that the chief raysat the edge of each ones FOV is parallel to the other.

FIG. 11 shows an imaging system with NP Point behind the image plane.

FIG. 12 shows a multiple unit imaging system with NP Points co-located.

FIG. 13 shows a 3-dimensional representation of a 360 degree lens systemwith edge rays constrained to lie along each dodecahedron face.

FIG. 14 shows a circle inscribed in a pentagon illustrating blind spotsthat would be created if lens was a circle rather than a pentagon.

FIG. 15 shows the first lens element of each system, initially designedto circumscribe regular pentagons.

FIG. 16 : The diameter of the first lens element is constrained to be1.7013a, where a is the side length of the regular pentagon.

FIG. 17 : The distance from the center of the first lens element to thecenter of the dodecahedron (NP Point) is 1.1135a where a is the sidelength of the pentagon.

FIG. 18 : The distance from the top of the pentagon face to the NP Pointis constrained to be 1.31a where a is the side length of the regularpentagon. Here the NP Point is the center of the dodecahedron.

FIG. 19 : Diagram illustrating the constraints imposed on the first lenselement with respect to the center of the dodecahedron. “a” is the sidelength of each regular pentagon in the dodecahedron.

FIG. 20 : Diagram illustrating that the maximal length of any element isconstrained to fit within the 31.717 degree half angle cone of lightemanating from the center of the dodecahedron.

FIG. 21 : Three-dimensional representation of 1/12th of dodecahedron andangle between center of dodecahedron and center of pentagon edge.

FIG. 22 : Three-dimensional representation of 1/12th of dodecahedron andangle between center of dodecahedron and edge of pentagon edge.

FIG. 23 : Pentagon shaped lens element showing height to ray 1 and ray37.

FIG. 24 : Zemax diagram of current lens design showing Rays 1 and 37 inmodel.

FIG. 25 : Three-dimensional Zemax diagram of current lens design fromback.

FIG. 26 : Three-dimensional Zemax diagram from side.

SUMMARY

An aspect of the invention is a multicamera panoramic imaging systemhaving no parallax. According to a non-limiting embodiment, themulticamera panoramic imaging system includes a plurality of discrete,imaging systems disposed in a side-by-side array, wherein a field ofview of each discrete, imaging system is conjoined with a field of viewof each adjacent discrete imaging system, further wherein a stencil ofchief rays at the edge of the field of view of any one of the discreteimaging systems will be substantially parallel to a stencil of chiefrays at the edge of the field of view of any adjacent ones of thediscrete imaging systems such that all of the substantially parallelstencils of chief rays appear to converge to a common point when viewedfrom object space. In various non-limiting embodiments, the multicamerapanoramic imaging system may include or be further characterized by thefollowing features, limitations, characteristics either alone or invarious combinations thereof:

-   -   comprising a plurality of identical discrete imaging systems;    -   wherein at least 50% of the stencil of chief rays deviate from        parallel by twenty degrees or less;    -   wherein each of the discrete imaging systems includes an image        sensor, further wherein the apparent convergence point lies        behind the image sensor of each of the discrete imaging systems;    -   wherein none of the discrete imaging systems physically overlap;    -   wherein the system has a dodecahedron geometry, further wherein        the system is characterized by a 360 degree FOV;    -   wherein a front lens of each of the discrete imaging systems is        a portion of a single, contiguous freeform optic;    -   wherein each image sensor is a wavefront sensor;    -   wherein each of the discrete imaging systems has a curved image        plane so as to match a distortion and Petzval Curvature of the        imaging system.

An aspect of the invention is a method for forming an image of an objecthaving no parallax. According to a non-limiting embodiment, the methodincludes providing a panoramic imaging system, wherein the panoramicimaging system comprises a plurality of discrete imaging systems eachcharacterized by a field of view; and constraining a stencil of chiefrays at the edge of the field of view of every one of the discreteimaging systems to be substantially parallel to a stencil of chief raysat the edge of the field of view of an immediately adjacent one of thediscrete imaging systems such that all of the parallel stencils of chiefrays appear to converge to a common point when viewed from object space,wherein the imaging system is parallax-free. In various non-limitingembodiments, the panoramic imaging method may include or be furthercharacterized by the following features, limitations, characteristics,steps either alone or in various combinations thereof:

-   -   further comprising constraining at least 50% of the stencil of        chief rays to deviate from parallel by twenty degrees or less;    -   further comprising using an algorithm to correct a distortion        aberration in a contiguous 360 degree image formed by the        imaging system.

An aspect of the invention is a method for designing a (substantially)parallax-free, panoramic imaging system. According to a non-limitingembodiment, the method includes determining an overall panoramic imagingsystem geometry, wherein the overall panoramic imaging system comprisesa plurality of discrete, imaging systems having respective fields ofview, disposed in a side-by-side array such that the fields of view ofadjacent imaging systems conjoin; designing the discrete imaging systemssuch that a stencil of chief rays at the edge of the field of view ofone of the discrete imaging systems will be substantially parallel to astencil of chief rays at the edge of the field of view of an adjacentone of the discrete imaging systems such that the substantially parallelstencil of chief rays would appear to converge to a common point whenviewed from object space. In various non-limiting embodiments, thepanoramic imaging method may include or be further characterized by thefollowing features, limitations, characteristics, steps either alone orin various combinations thereof:

-   -   wherein the overall panoramic imaging system comprises a        plurality of identical discrete imaging systems;    -   wherein in designing the discrete imaging systems, ensuring that        there is no physical overlap between any of the plurality of the        discrete imaging systems;    -   wherein in designing the discrete imaging systems, ensuring that        the apparent convergence point lies behind a respective image        sensor of each discrete imaging system.

DETAILED DESCRIPTION OF EXEMPLARY, NON-LIMITING EMBODIMENTS

For a panoramic camera to achieve minimal parallax, the field of views(FOV) of the imaging systems must not overlap. Thus, the chief ray atthe edge of the FOV must approach the optical system parallel to thechief rays at the edge of the adjacent optical system.

FIG. 6 illustrates two imaging systems 110 side by side which do nothave parallax. The chief rays 140 at the edge of each system areconstrained to lie parallel one another. Thus, objects lying along thisline are imaged to the same point in the image plane 115. This is anapproach that can be used to design the individual lens elements. Thefields of view 130 do not overlap one another because the chief rays 140at the blending angles are constrained to be parallel to one another andconverge to a common point 160. The common point 160 will depend on thegeometry in which the lenses 110 are encased. In other words, the chiefrays 140 are constrained to be parallel such that they appear to crossthe optical axis 120 at the same point when viewing the lens system 110from object space 135. In actuality, they cross the optical axis 120 atan image sensor 125, which lies before this imaginary point, but itappears, looking into the lens system 110 from object space 135, thatthey cross at the same point.

NP Point (No Parallax Point)

To aid in the understanding of the previous concept, we define a termreferred to as the No Parallax Point (NP Point). The NP Point 160 is anabstraction used for understanding how the chief rays 140 at the edge ofthe FOV 130 can physically be made to lie parallel to one another andwhat rules they should follow. The NP Point 160 is the point where thechief rays 140 at the edge of adjacent optical systems 110 intersect theoptical axis when viewing the system from object space 135 for apanoramic imaging system 100 without parallax.

According to the embodied invention, the NP Points for each imagingsystem must lie in the same location. That is to say, that the rays ofadjacent optical systems must be parallel. FIG. 9 shows an imagingsystem 25 with the NP Point 60 lying in front of the imaging sensor 40.FIG. 10 illustrates two imaging systems 25 aligned such that the chiefrays 20 at the edge of each one's FOV 28 is parallel to the other. Thisconstraint means that the NP Point 60 must be at the same location forboth systems. When the NP Point 60 is in front of the image sensor 40,it is impossible to align the NP Points 60 without the lens elementsoverlapping. This system would not have any parallax, but it isphysically impossible to implement. This indicates that when designingthe optical system, the NP Point should lie behind all of the elementsin the imaging system so that no elements physically overlap with oneanother.

FIG. 11 shows a system 210 where the NP Point 260 lies behind the imageplane 215. When this is the case, it is possible to arrange multipleimaging systems 210 such that the fields of view 230 do not overlap, asshown in FIG. 12 . The exact location of the NP Point 260 will bedetermined by the geometry of the lens arrangements. By arbitrarilypicking a location, that is to say arbitrarily choosing a ray height andincident angle such that the chief ray 240 appears to cross the opticalaxis 220 behind the image plane 215, the geometry of lens systems mayrequire hundreds of lens units to capture a full 360 degree image. TheNP Point location must be determined after considering the geometry onemay wish to use for the lenses (210).

An embodiment of the present invention relates to a multicamerapanoramic imaging system 100, where the fields of adjacent imaging units110 merge to form the composite field of view of the entire imagingsystem, as illustrated in the schematic of FIG. 7 . Traditionalpanoramic imaging systems 50 put together imaging units 25 in such a waythat their respective fields of view 28 overlap as illustrated in theschematic of FIG. 8 , which leads to parallax in the resulting images,and requires corrective software to stitch the images together to removethe parallax.

In the instant exemplary embodiment, the rays striking the edge of oneimaging unit are constrained to lie parallel to the incoming rays of anadjacent imaging unit so that both imaging systems share the same set ofedge rays. As seen in the 3-dimensional model of FIG. 13 , the rays 240at the edge 250 of one imaging unit 210 are the same as those at theedge 250 of an adjacent imaging unit 210. The rays are the gray linesconstrained to lie along the surface of the dodecahedron edge. The grayrays at the edge of each pentagon shaped lens 265 are coincident to therays entering its neighboring surface. All rays at radii beneath theedge rays lie at smaller angles of incidence so that these rays do notoverlap rays from adjacent systems 300.

The embodied panoramic imaging system 200 utilizes the aforementionedtechnique of designing an imaging system with a NP point 260 behind theimage sensor (225), and combines multiple lens systems (210) in adodecahedron geometry, to create a 360 degree FOV camera (200) withminimal or no parallax.

The first lens element 270 will be shaped into the surface of a regularpentagon 267. The complete system will be composed of 12 discreteimaging units 210, each with a common NP point 260 for rays along theedge of the pentagon 267 and constrained to have incident angles meetingthe geometry specified by that of a dodecahedron.

A dodecahedron is a polyhedron with 12 surfaces. A polyhedron is a threedimensional solid consisting of a collection of polygons joined at theedges. Each side of the dodecahedron is a regular pentagon (a pentagonwith equal length sides). Dodecahedrons have some important geometricalproperties that must be understood in order to design a lens system 210utilizing the geometry. The properties will be discussed in turn nextafter briefly discussing why the first lens must be shaped into thesurface of a pentagon.

By using a circularly edged lens as the first element 270 in thedodecahedron geometry, it is not possible to capture all information inthe 360 degree field of view using the current technique of aligningedge rays. The missing area from where the first lens 270 is inscribedin the pentagon 267 (shaded region in FIG. 14 ) creates blind spots.Because the fields of view 230 never overlap, this information is nevercaptured. It can be calculated that the ratio between the area of acircle to the area of a pentagon 267 it is inscribed in is equal to π/5or 62.83%. This is the maximal amount of information that we can recordfor the 360 degree field around us. Blind spots created between the lensand the pentagon delete nearly 40% of information in the 360 degreeimage.

The following description is meant to illustrate the geometry of adodecahedron and is necessary when creating a lens system 210 utilizingthe aforementioned NP technique and a dodecahedron geometry, but is notessential for the purposes of creating the no parallax, panoramicimaging system 200 embodied herein.

Property 1: Diameter of Circle Circumscribing Regular Pentagon

For each of the 12 individual lens systems 210, the first lens 270 willbe designed such that it circumscribes each of the regular pentagons 267of the dodecahedron as shown in FIG. 15 . The diameter of a circlecircumscribing a regular pentagon is:

D=a/sin(36°)=1.7013a

In the equation above, “a” is the side length of the regular pentagon.The first lens element 270 of each system (210) will fully circumscribeeach pentagon 267 and so the diameter of the first lens element 270 foreach system (210) is given as 1.7013a as illustrated in FIG. 16 .

Property 2: Inscribed Sphere Touching Center of Each Pentagon

The radius of an inscribed sphere (tangent to each of the dodecahedron'sfaces) is:

$r_{i} = {{a\frac{1}{2}\sqrt{\frac{5}{2} + {\frac{11}{10}\sqrt{5}}}} \approx {{1.1}135{16364 \cdot a}}}$

This radius is the distance from the center 280 of the dodecahedron,which will be the NP Point 260 for each lens (210) in this design, andthe center of the pentagon's face, which coincides with the center(optical axis) of the first lens element 270 in a system occupying thatpentagon. This point is at the center of each pentagon face. The lengthbetween the NP point 260 and the center of the dodecahedron isconstrained to be 1.1135a where a is the length of one of the pentagonsides, as illustrated in FIG. 17 .

Property 3: Mid-Radius of Dodecahedron

The mid-radius is the point connecting the center of the dodecahedronand the middle of each edge. This length is given as follows:

$r_{m} = {{a\frac{1}{4}\left( {3 + \sqrt{5}} \right)} \approx {{1.3}090{16994 \cdot a}}}$

This equation constrains the distance between the top of the pentagonface and the NP Point, as illustrated in FIG. 18 .

Constraints

The geometric properties of a dodecahedron constrain the design of the12 lenses (210) that will embody it. In particular, we have thefollowing four parameters based upon the description given above:

1. Diameter of 1st lens element 270: 1.7013a;

2. Distance from 1st lens element 270 to center of dodecahedron:1.1135a;

3. Distance from top of 1st lens element 270 to center of dodecahedron:1.31a;

4. FOV=37.3777 degrees Given any two of the first three constraints, wehave that the angle between the optical axis 220 of the lens (210) andthe top of the first lens element 270 is 37.3777 degrees (see FIG. 19 ):

tan⁻¹((1.7013/2)/1.1135)−37.377°

We want this angle of 37.37 degrees to be the field of view 230 of thelens (210). This will ensure that the NP Point 260, that is the pointwhere the chief ray 240 of the blending (the blending angle being thefull FOV) intersects the optical axis 220 in object space 235, lies atthe center 280 of the dodecahedron. All of the other constraints willensure that the lens elements 278 lie before the NP Point 260 and thatthe elements 278 fall within the 31.717 degree half angle cone of light.

Diameter of Other Lens Elements and Sensor

With the four constraints given above, we know what the size of eachlens element 278 after the first (270) must be in order to fit into thedodecahedron geometry. In order for the preceding lens elements (278) tofit, any lens or sensor element must fit inside of the 31.717 degreecone of light beginning at the center of the dodecahedron and tangentialto the diameter of the first lens element 270. As the distance from thefirst lens element 270 increases, the diameter of the preceding lenselements 278 will decrease proportionally (see FIG. 20 ).

The maximum diameter of any lens element 278 or sensor (225) precedingthe first can be found geometrically to be less than or equal to(1.1135a−D)*tan(31.716 degrees) where D is the distance of that elementfrom the first lens element 270.

Thus, we now have the five constraints that will allow this lens system210 to match the geometry of a dodecahedron and permit 360 degreeimaging:

-   -   1. Diameter of 1st lens element 270: 1.3763a;    -   2. Distance from 1st lens element 270 to center of dodecahedron:        1.1135a;    -   3. Distance from top of 1st lens element 270 to center of        dodecahedron: 1.31a;    -   4. FOV=37.377 degrees;    -   5. φ_(Li)<(1.1135a-D_(L1,Li))tan(31.717°),        where φ_(Li) is the diameter of any lens element separated by a        distance D_(L1,Li) from the first. Given the above five        constraints, where all lenses are designed such that they fall        within the 31.717 degree cone of light emanating from the center        280 of the dodecahedron, it is possible to construct a lens        system 210 without parallax.

System Design

A geometry for the lenses (210) was chosen. Platonic solids have theproperty that they are composed of many solids of equal geometry andvolume. For a system imaging 360 degrees, this allows the compositeimaging system to be made from the same replicated lens design. Adodecahedron geometry was chosen because it is approximately sphericalin its geometry.

In order for the edge rays of one imaging unit 210 to lie parallel tothose of an adjacent unit, they must enter at the same angle. The angleshared by both imaging units is that of the dodecahedrons edge surface.At the center of the edge surface, the angle with respect to the centerof the dodecahedron center is 31.717 degrees, as illustrated in FIG. 21. At the corner of the edge surface, the angle with respect to thecenter of the dodecahedron center 280 is 37.377 degrees, as illustratedin FIG. 22 .

In order to make the rays along adjacent imaging units 210 match, thefirst lens 270 of the imaging unit 210 is cut into a pentagon 267,matching the surface of the dodecahedron. At the center of the edge, theray 240 striking the surface enters with an angle of incidence of 31.717degrees. At the corner of the edge, the angle of incidence of anentering ray is 37.377 degrees. At all points along the edge of the lens(270), the angle of incidence of an entering ray is made to match thegeometry of the dodecahedron surface.

The angle of incidence for 37 rays along the edge of the pentagon lenswas calculated using trigonometry, knowing the distance from the centerof the dodecahedron to the center of the pentagon face, and knowing thedistance from the center 280 of the dodecahedron to the edge point inquestion as shown in the FIGS. 21 and 22 . The height of each ray wasconstrained to lie along the pentagon edge. For example, with a radiusof 120 mm describing the circumscribed circle of surface 1, the ray atpoint 1 has a height of 48.54 mm and an angle of incidence of 31.717degrees. The ray at point 37 has a height of 60 mm and an angle ofincidence of 37.377 degrees. Table I describes the values for rayheights and angle of incidence for 37 points between Point 1 and Point36 in FIG. 23 .

TABLE I (Data showing constraints on 37 rays 240 lying along the edge ofthe first lens 270) Point Ray Height 245 Angle of Incidence 1−48.54101966 31.71747441 2 −48.55131914 31.72137741 3 −48.5822044631.7330904 4 −48.6336364 31.75262531 5 −48.70554989 31.78000204 6−48.79785436 31.81524851 7 −48.91043437 31.8584007 8 −49.0431502831.90950275 9 −49.19583915 31.96860698 10 −49.36831565 32.03577404 11−49.56037318 32.111073 12 −49.77178508 32.19458149 13 −50.0023058532.28638584 14 −50.25167251 32.38658121 15 −50.51960599 32.49527181 16−50.80581256 32.61257109 17 −51.10998523 32.7386019 18 −51.4318052432.87349676 19 −51.77094349 33.01739809 20 −52.12706197 33.17045845 21−52.49981514 33.33284086 22 −52.88885128 33.50471903 23 −53.293813833.68627773 24 −53.7143425 33.87771306 25 −54.1500747 34.07923284 26−54.60064642 34.29105695 27 −55.0656934 34.51341771 28 −55.5448520634.74656026 29 −56.03776039 34.99074298 30 −56.54405884 35.2462379 31−57.06339098 35.51333115 32 −57.59540424 35.7923234 33 −58.1397505136.0835303 34 −58.69608667 36.38728295 35 −59.26407504 36.70392839 36−59.84338384 37.03383003 37 −60 37.37736813

A diagram illustrating the ray constraints is shown in FIG. 24 . Ray 1has a height of 48.54 mm and an angle of incidence of 31.717 degrees.Ray 1 is the ray going through point 1 in FIG. 24 . Ray 2 has a heightof 60 mm and an angle of incidence of 37.377 degrees and is the raygoing through point 37 in FIG. 24 . All 37 rays 240 are constrained bythe ray heights 245 and angles specified in the table above. Constrainedin this way, all rays 240 enter the lens 270 at the same angle as thesurface of the dodecahedron. Looking at those same rays in another way,we can see that the rays are constrained properly to a pentagon geometryat the correct angles of incidence, as illustrated in FIGS. 25 and 26 .

PARTS LIST

-   -   10 optical system    -   12 object    -   14 image    -   16 optical axis    -   18 aperture stop    -   20 chief ray    -   25 imaging system, optical system, camera, imaging unit    -   28 field of view (FOV)    -   35 object space    -   40 imaging sensor, image sensor    -   50 360 degree imaging system, panoramic imaging system    -   60 NP point    -   100 panoramic imaging system    -   110 imaging system, lenses, lens system, imaging unit    -   115 image plane    -   120 optical axis    -   125 image sensor    -   130 field of view, FOV    -   135 object space    -   160 NP point, common point    -   170 front lens    -   200 panoramic imaging system    -   210 discrete imaging system, imaging system, imaging unit, lens        system    -   215 image plane    -   220 optical axis    -   225 image sensor    -   230 field of view, FOV    -   235 object space    -   240 ray, chief ray    -   242 refracted chief rays    -   245 ray heights    -   250 edge    -   260 NP point, common point    -   265 pentagon shaped lens    -   267 pentagon    -   270 front lens, first lens, first lens element, first element,        1^(st) lens element    -   272 second lens group    -   274 third lens group    -   276 aperture stop    -   278 lens elements    -   280 center    -   290 dodecahedron    -   300 adjacent systems, side by side array    -   310 wavefront sensor

1. A method for generating a polygonal and conical shaped field of view in a lens system, comprising: providing a first lens element in the lens system with a polygonal shape and a plurality of edges, each of the edges having a plurality of edge surface angles relative to an optical axis of the lens system; and aligning a field of view of the lens system with the polygonal shape of the first lens element and the plurality of edge surface angles along the edges of the first lens element to provide the polygonal and conical shaped field of view.
 2. The method of claim 1, further comprising the step of cutting the first lens element into the polygonal shape.
 3. The method of claim 1, wherein the step of aligning the field of view comprises applying a plurality of ray position and ray angle constraints along the plurality of edges to align the field of view of the lens system with the polygonal shape of the first lens element and the plurality of edge surface angles along the edges of the first lens element.
 4. The method of claim 1, wherein the polygonal shape is a pentagon.
 5. The method of claim 1, wherein the polygonal field of view has an angular half width that is from about 31-degrees wide to about 37-degrees wide.
 6. The method of claim 1, further comprising forming an image having a polygonal shape at an image plane with the polygonal and conical shaped field of view.
 7. An imaging system, comprising: an outer lens element having a polygonal shape with a plurality of edges, each of the edges having a plurality of edge surface angles relative to an optical axis of the imaging system, the imaging system configured to provide a field of view having a polygonal and conical shape matching the plurality of edge surface angles.
 8. The imaging system of claim 7, wherein the imaging system is configured to align a field of view of the imaging system with the polygonal shape of the outer lens element and the plurality of edge surface angles along the edges of the outer lens element
 9. The imaging system of claim 7, wherein the imaging system is constrained to have a plurality of chief rays that form the polygonal and conical shaped field of view and correspond to the polygonal shape and the plurality of edge surface angles of the outer lens element.
 10. The imaging system of claim 7, wherein the imaging system is configured to apply a plurality of ray position and ray angle constraints along the plurality of edges to align the field of view of the image system with the polygonal shape of the outer lens element and the plurality of edge surface angles along the edges of the outer lens element.
 11. The imaging system of claim 7, wherein the field of view has an angular half width that is from about 31-degrees wide to about 37-degrees wide.
 12. The imaging system of claim 7, wherein the polygonal shape is a pentagon.
 13. The imaging system of claim 7, wherein the field of view projects toward an NP Point located behind a focal plane of the imaging system.
 14. A multicamera imaging system, comprising a first imaging system and a second imaging system configured adjacent to each other, each comprising an outer lens element having a polygonal shape with a plurality of edges, each of the edges having a plurality of edge surface angles relative to an optical axis of the imaging system, the imaging system configured to provide a field of view having a polygonal and conical shape; the polygonal and conical shaped field of view of the first imaging system merging with the polygonal and conical shaped field of view of the second imaging system along one of the edges to form a combined image having minimal or no parallax.
 15. The multicamera imaging system of claim 14, wherein the first imaging system and the second imaging system are each configured to apply a plurality of ray position and ray angle constraints along the plurality of edges to align the field of view of the first imaging system and the field of view of the second imaging system with the polygonal shape of the outer lens element and the plurality of edge surface angles along the edges of the outer lens element.
 16. The multicamera imaging system of claim 14, wherein the first imaging system and the second imaging system are each constrained to have a plurality of chief rays that form the polygonal and conical shaped field of view and correspond to the polygonal shape and the plurality of edge surface angles of the outer lens element.
 17. The multicamera imaging system of claim 14, wherein the plurality of chief rays from the first imaging system and the second imaging system, when viewed from object space, appear to converge towards a common NP point.
 18. The multicamera imaging system of claim 14, wherein the polygonal shape of the first lens element is a pentagon.
 19. The multicamera imaging system of claim 14, wherein the polygonal field of view has an angular half width that is from about 31-degrees wide to about 37-degrees wide. 